I've been told that acceleration orthogonal to an objects movement direction doesn't require energy. Thus when a satellite goes around the earth, the change in direction caused by gravity doesn't use any energy.
But, say we remove the earth and we still want the satellite to go in its usual circular pattern, then we need to mount a vector thruster (rocket) on the satellite and keep it thrusting continuously to maintain the circular pattern. This rocket thrust will require energy, even if it thrusts perfectly orthogonal to the direction of movement of the satellite.
Thus we have two scenarios with the exact same movement pattern, but in one scenario it takes no energy to uphold the pattern, and in the second scenario it takes continuous energy consumption to uphold the pattern.
How come gravity is said to use no energy in its maintenance of the circular movement pattern?
EDIT: Both scenarios has to uphold Newtons first law (conservation of inertia). The earth scenario does it by moving the earth ever so slightly in opposite way to the satellite. The rocket scenario does it by shooting gas into space at high velocity. However, in both cases something happens in order to conserve inertia (in opposition to nothing). Thus, arguing that the rocket spends energy to conserve the inertia of the turning satellite does nothing to answer why the earth doesn't have to spend energy as well, to conserve inertia of the turning satellite. Even arguing that the rocket is inefficient (waste heat) wouldn't answer that question.
EDIT 2: The rope scenario seems to be isomorphic to the earth scenario: the only difference is that the weak gravitational force has been replaced with the stronger nuclear forces that holds the rope together.